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Question

Find the volume of the parallelopiped whose coterminals edges are represented by the vectors
a=^i2^j+^3b=2^i+3^j4^kc=^i3^j+5^k

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Solution

Consider the problem
as we know that area of parallelopiped whose three sides are a,b and c equal to

[abc]

And as we have

a=^i2^j+3^kb=2^i+3^j4^kc=^i3^j+5^k

Now,

[abc]=∣ ∣123234135∣ ∣

=1(1512)+2(10+4)+3(63)

=312+9=0
Hence volume =0 sq. units


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